Scanning probe microscopes such as atomic force microscopes are widely used for imaging the surface of samples at the atomic level; however, these microscopes are not well suited for measuring the deformation properties of samples at these levels. Scanning probe microscopes enable a class of imaging techniques in which a tip that interacts locally with a sample is scanned over the surface of the sample to generate a three-dimensional image representing the properties of the surface. The tip is typically mounted on a cantilevered arm having a fixed end that can be moved vertically relative to the sample. For example, in contact mode atomic force microscopy, as the tip is moved over the surface of the sample, the arm deflects in response to changes in the topology of the surface. The vertical position of the cantilever arm relative to the sample is adjusted to maintain the arm in a predetermined state. The vertical position as a function of position on the sample can then be used to provide an image of the surface. Typically, scanning force microscopes seek to minimize the deformation of the sample.
In the AC, or non-contact mode, the tip and arm are oscillated at a frequency near the resonant frequency of the arm. The height of the tip can be controlled such that the tip avoids contact with the sample surface, sampling short-range tip/sample forces or the tip can be allowed to make light intermittent contact with the sample only at the bottom of the oscillation cycle. Contact between the probe tip and the sample results in an alteration of the amplitude, phase and/or frequency of the oscillation. The controller adjusts the height of the probe over the sample such that the oscillation amplitude, phase and/or frequency is kept at a predetermined constant value.
There are a number of applications in which the deformation of the sample as a function of an applied force must be measured. The areas to be sampled are of the dimensions of a scanning probe tip. Scanning probe microscopes are poorly suited for such measurements. The force that is applied by the tip to the surface of the sample is determined by the deflection of the cantilever arm. As the fixed end of the cantilever arm is moved toward the sample while the tip is in contact with the sample, the arm bends and a greater force is exerted, and the arm bends further. Part of the force causes the tip to penetrate the sample, and part of the force deforms the arm. The force applied at the tip depends on the bending of the arm; hence, to determine the force, the degree of bending of the arm must be accurately measured, and the arm must be calibrated. In addition, the degree of penetration of the tip into the arm must be independently measured. Such measurements present significant challenges.
To overcome these problems, a class of devices referred to as “nanoindenters” has been developed. In a nanoindenter, the force that is applied to the tip is independent of the position of the tip relative to the sample surface. Such measurements require displacement measurement with accuracies in the nanometer range. Forces of the order of 10 mN are applied to a tip having a radius of curvature of the order of 100 nm. These measurements can be used to determine the mechanical properties of the sample such as the elastic modulus and hardness.
In one class of nanoindenter, the tip is mounted on one end of a rod. The other end of the rod includes a mechanism for generating a known force to the rod. A separate position measuring mechanism is used to determine the position of the end of the rod. Typically, the position is determined by measuring the change in capacitance of a capacitor having one plate attached to the rod and the other plate fixed with respect to the apparatus. In one prior art arrangement, a three-plate structure is utilized in which the moveable plate is between two fixed plates and changes in the ratio of the capacitances is measured.
While such nanoindenters provide significant improvements over a scanning probe microscope for making deformation measurements, these designs are subject to other problems. First, the measurement of the tip position by measuring the position of the rod assumes that the length of the rod remains constant during the course of the measurements. The distances being measured are of the order of nanometers. Hence, changes in length of the arm due to the thermal expansion or contraction of the rod itself over the course of the measurements can introduce significant errors.
Second, the accuracy of the capacitive position measurements is insufficient for many applications and the time needed between measurements can be excessive. Capacitance measurements typically involve measuring the shift in the resonant frequency of a circuit having the capacitor in question as an element thereof. The settling time for such measurements after changes in the capacitance can increase the time between measurements if high accuracy is needed. Hence, in applications in which a detailed map of the properties of a surface is to be measured, the scanning time can be excessive.